A firm’s short-run revenue is given by R = 10e - e², where e is the level of effort by a typical worker (all workers are assumed to be identical). A worker chooses his level of effort to maximize wage less effort w - e (the per-unit cost of effort is assumed to be 1). Determine the level of effort and the level of profit (revenue less wage paid) for each of the following wage arrangements. Explain why these different principal-agent relationships generate different outcomes.

a. w = 2 for e ³ 1; otherwise w = 0.

b. w = R/2.

c. w = R - 12.5.